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**2008/286**

**Title:**

One-Up Problem for (EC)DSA

**Authors:**
Daniel R. L. Brown

**Abstract:**

The one-up problem is defined for any group and a function from the group to integers. An instance of problem consists of two points in the group. A solution consists of another point satisfying an equation involving the group and the function. The one-up problem must be hard for the security of (EC)DSA. Heuristic arguments are given for the independence of the discrete log and one-up problems. DSA and ECDSA are conjectured to be secure if the discrete log and one-up problems are hard and the hash is collision resistant.

**ePrint:**
https://eprint.iacr.org/2008/286

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